What approximate value will come in place of the question mark (?) in the following question? (You are not expected to calculate the exact value)
`(6.02)^2 - sqrt(120.89)+sqrt(144.06)= ?`

Options

A. 35
B. 42
C. 37
D. 40

Explanation

To solve the expression \( (6.02)^2 - \sqrt{120.89} + \sqrt{144.06} \) and find the approximate value, we can follow these steps:

### Step 1: Approximate \( (6.02)^2 \)

Since \( 6.02 \) is close to \( 6 \), we can approximate:

\[ (6.02)^2 \approx (6)^2 = 36 \]

### Step 2: Approximate \( \sqrt{120.89} \)

Next, we approximate \( \sqrt{120.89} \). The nearest perfect square to \( 120.89 \) is \( 121 \):

\[ \sqrt{120.89} \approx \sqrt{121} = 11 \]

### Step 3: Approximate \( \sqrt{144.06} \)

Now, we approximate \( \sqrt{144.06} \). The nearest perfect square to \( 144.06 \) is \( 144 \):

\[ \sqrt{144.06} \approx \sqrt{144} = 12 \]

### Step 4: Substitute the approximations into the expression

Now we can substitute our approximations back into the original expression:

\[ (6.02)^2 - \sqrt{120.89} + \sqrt{144.06} \approx 36 - 11 + 12 \]

### Step 5: Calculate the final result

Now, we perform the arithmetic:

\[ 36 - 11 + 12 = 36 - 11 = 25 \]
\[ 25 + 12 = 37 \]

Thus, the approximate value that comes in place of the question mark (?) is:

\[ \boxed{37} \]

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